102f05mt2

# 102f05mt2 - B U Department of Mathematics Math 102 Calculus...

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B U Department of Mathematics Math 102 Calculus II Fall 2005 Second Midterm This archive is a property of Bo˘ gazi¸ci University Mathematics Department. The purpose of this archive is to organise and centralise the distribution of the exam questions and their solutions. This archive is a non-proﬁt service and it must remain so. Do not let anyone sell and do not buy this archive, or any portion of it. Reproduction or distribution of this archive, or any portion of it, without non-proﬁt purpose may result in severe civil and criminal penalties. 1. Find the derivative of f ( x, y, z ) = x 3 + y 3 z at ( - 1 , 2 , 1) in the direction toward (0,3,3). Solution: A vector in the indicated direction is (0 , 3 , 3) - ( - 1 , 2 , 1) = < 1 , 1 , 2 > . The unit vector in that direction is ~u = 1 6 < 1 , 1 , 2 > ~ O f ( x, y, z ) = < 3 x 2 , 3 y 2 z, y 3 > ~ O f ( - 1 , 2 , 1) = < 3 , 12 , 8 > Hence, the derivative of f ( x, y, z ) = x 3 + y 3 z at ( - 1 , 2 , 1) in the direction toward (0,3,3) is

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## This note was uploaded on 04/30/2008 for the course C CMPE 150 taught by Professor Tuna during the Spring '08 term at Boğaziçi University.

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102f05mt2 - B U Department of Mathematics Math 102 Calculus...

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